Question

A positive point charge Q1 = 1.6 ? 10-5 C is fixed at the origin of coordinates, and a negative charge Q2 = -5.5 ? 10-6 C is fixed to the x axis at x = +2.0 m. Find the location of the place(s) along the x axis where the electric field due to these two charges is zero. (Enter the locations in order from -x to +x. If there is only 1 location, enter 0 in the second box.)

Answer 1

The electric field from a charge is E = K*q/x^2

The field from the charge at the origin along the x-axis is

K*Q1/x^2.

The field from charge Q2 measured from the origin is

K*Q2/(x - d)^2, where d is the distance from the origin.

You want to find the point x0 where the field is zero, therefore the field from Q1 plus the field from Q2 must add to 0:

K*Q1/x0^2 + K*Q2/(x0 - d)^2 = 0

Q1/x0^2 + Q2/(x0 - d)^2 = 0

Put in 1.6*10^-5 for Q1 and -5.5*10^-6 for Q2 and 2.0 for d and solve for x0

1.6*10^-5 / x0^2 - 5.5*10^-6 / (x0 - 2)^2 = 0

1.6*10^-5*(x0 - 2)^2 - 5.5*10^-6*x0^2 = 0

1.6*10^-5*x0^2 - 4*1.7*10^-5*x0 + 4*1.7*10^-5 - 5.5*10^-6*x0^2 = 0

(1.6*10^-5 - 6.5*10^-6)*x0^2 - 6.8*10^-5*x0 + 6.8*10^-5 = 0

1.05*10^-5*x0^2- 6.8*10^-5*x0 + 6.8*10^-5 = 0

1.05*x0^2 - 6.8*x0 + 6.8 = 0

x = 5.24 or x = 1.24

since the charges are of opposite sign, locations in between the charges (from x =0 to x = 2) the fields are in the same direction and cannot sum to 0, therefore the answer must be x0 = 5.24 m